If \( \int \frac{5 x+4}{\sqrt{x^{2}+2 x+5}} d x=\left(x^{2}+2 x+5\right)^{1 / 5}+f(x)+c \) then ....

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If \( \int \frac{5 x+4}{\sqrt{x^{2}+2 x+5}} d x=\left(x^{2}+2 x+5\right)^{1 / 5}+f(x)+c \)
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then \( f(x) \) is equal to
(1) \( \frac{1}{2} \log _{e}\left(x+1+\sqrt{x^{2}+2 x+5}\right) \)
(2) \( -\log _{e}\left(x+1+\sqrt{x^{2}+2 x+5}\right) \)
(3) \( -\frac{1}{2} \log _{e}\left(x+1+\sqrt{x^{2}+2 x+5}\right) \)
(4) \( \frac{(x+1)}{2} \sqrt{x^{2}+2 x+5} \)


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